Spatially distributed networks (SDNs) consist of a large amount of agents, and each agent
is equipped with subsystems for limited data processing and direct communication link to its “neighboring" agents
within communication range.
SDNs appear in (wireless) sensor networks,
smart grids, social network and many real world applications
[1]}–[2]}.
In this letter, we describe the topological structure of an SDN by a finite graph
\({\mathcal {G}}:=(V, E)\) , and its communication range \(L\)  by the maximal geodesic distance
such that direct communication link between agents \(i,j\in V\)  exists whenever
\(\rho (i,j)\le L\) , where the geodesic distance
\(\rho (i,j)\)  is the number of edges in a shortest path connecting \(i, j\in V\) .
As SDNs do not have a central facility,
data processing on SDNs
should be designed at the agent/vertex level with direct data exchanging between neighboring vertices in the communication range.
